Measurements with single dish telescopes with (for that time) very
sensitive receivers provided the first hints that rotation curves
stay flat at large radii. In particular, there was a debate about the
rotation curve of M31 at large radii (cf.
Roberts 1975,
Emerson & Baldwin
1973, and
Baldwin 1975),
but also about possible sidelobe effects
of Arecibo data (see discussion after
Salpeter 1978).
Interferometer
data free from this effect for 5 Scd galaxies
(Rogstad & Shostak 1972)
showed that rotation curves did not decline. Newer data for
a number of galaxies observed with the Westerbork telescope settled
these issues : a compilation of 25 rotation curves of spiral galaxies of
various morphological types showed that all of them are roughly flat,
or rising (cf.
Bosma 1978,
1981a,
b).

Numerical simulations of spiral galaxies also started in earnest in
the early 1970s.
Hohl (1971)
found consistently that flat disks
are very prone to the bar instability. A cure was devised by
Ostriker & Peebles
(1973),
i.e. to embed a disk in a dynamically hot dark
halo, which was presumed to be roughly spherical.
The required halo masses interior to the disks are rather
large, so that the total mass of a large galaxy at large radii can
be easily 1012M. The absence of a decline in a
rotation curve implies that mass increases linearly with radius.
In this way a mass radius relationship can be established, e.g. for
our Galaxy, using various tracers of the mass like outlying globular
clusters, satellites, Local Group timing, etc.
(Ostriker et al. 1974).

The data in the late seventies from HI observations
(Bosma 1978),
show that extended flat rotation curves are ubiquitous for large spirals,
and that only for small Sc galaxies the rotation curves are still
rising. In a series of papers by Rubin et al.
(1978,
1980,
1982,
1985)
on H rotation curves a nice
systematic behaviour as function
of type and luminosity of the rotation curves for Sa, Sb and Sc
spirals was established as well.